Here is a response from the Hawaii Cruise Concierge at The Aloha Tower has to say....
Aloha Tower Marketplace forwarded your inquiry.
On "turnaround" days (when a ship is unloading passengers in the morning and boarding new passengers in the afternoon), there is usually a luggage day-storage service outside of Pier 10 (right next to Pier 11 at Aloha Tower). If you provide a specific date and cruise line, we can be more specific.
Please contact us at the information below if we may be of further service.
Mahalo and with best regards,
Hawaii Cruise Concierge
Aloha Tower Marketplace
1 Aloha Tower Drive, Mailbox 46
Honolulu, Hawaii 96813 USA
Telephone (808) 523-TOUR (8687)
Facsimile (808) 523-8687